Twelve-cornered strengthening member

ABSTRACT

A crush can to an automotive vehicle has a twelve-cornered cross section comprising sides and corners creating internal angles and external angles. A geometry of the cross section varies between a front section and a rear section of the crush can. The geometry of the cross section is optimized using a plurality of control parameters including a lateral width, a vertical width, a taper ratio, a front scaling factor, and a rear scaling factor.

This application is a divisional of U.S. patent application Ser. No.12/891,801, filed Sep. 27, 2010, which is a continuation-in-part of U.S.patent application Ser. No. 12/233,808, filed Sep. 19, 2008 (now U.S.Pat. No. 8,539,737), the entire content of each of which is incorporatedherein by reference.

INTRODUCTION

The present teachings relate generally to a strengthening member for avehicle body or other structures. The present teachings relate morespecifically to a strengthening member having a twelve-cornered crosssection.

BACKGROUND

It is desirable, for vehicle strengthening members, to maximize impactenergy absorption and bending resistance while minimizing mass per unitlength of the strengthening member.

When a compressive force is exerted longitudinally on a strengtheningmember, for example a force due to a front impact load on a vehicle'sfront rail or other strengthening member in the engine compartment, thestrengthening member can crush in a longitudinal direction to absorb theenergy of the collision. In addition, when a bending force is exerted ona strengthening member, for example a force due to a side impact load ona vehicle's front side sill, B-pillar or other strengthening member, thestrengthening member can bend to absorb the energy of the collision.

U.S. Pat. No. 6,752,451 discloses a strengthening member having concaveportions at the four corners of a basic rectangular cross section,resulting in four U-shaped portions forming an angle of 90 degrees witheach other. To avoid cracks at the concave portions at the four cornersand to increase strength, the concave portions have increased thicknessand hardness. Increased thickness and hardness of the corner portions isdisclosed to be achievable only by drawing or hydroforming, andtherefore decreases manufacturing feasibility while increasing the massper unit length of the strengthening member.

U.S. Pat. No. 6,752,451 makes reference to Japanese Unexamined PatentPublication No. H8-337183, which also discloses a strengthening memberhaving concave portions at the four corners of a basic rectangular crosssection, resulting in four U-shaped portions forming an angle of 90degrees with each other. U.S. Pat. No. 6,752,451 states that itsthickened concave portions provide improved crush resistance andflexural strength over H8-337183.

It may be desirable to provide a strengthening member configured toachieve the same or similar strength increase as provided by thethickened corners, while minimizing mass per unit length of the memberand maintaining a high manufacturing feasibility.

It may further be desirable to provide a strengthening member that canachieve increased energy absorption and a more stable axial collapsewhen forces such as front and side impact forces are exerted on thestrengthening member. Additionally, it may be desirable to provide astrengthening member that possesses improved noise-vibration-harshnessperformance due to work hardening on its corners.

In various applications, a strengthening member can be used as a crushcan attached directly to a bumper beam in alignment with a vehicle'sfront rails. Crush cans may, for example, manage impact energy andintrusion during a frontal collision. To protect a vehicle's occupantsin high speed crash events, a crush can (as part of a vehicle's frontend) acts as an energy absorber to absorb a maximum amount of impactenergy within a limited crush distance (i.e., a crush can must absorb ahigh amount of impact energy over a short crush distance). To minimizevehicle repair costs in low speed crash events, however, a crush canmust both absorb energy with a limited stroke and be sequentiallycollapsible within a low speed protection zone to avoid damage to costlyvehicle components.

It may be desirable, therefore, to provide a method of optimizing astrengthening member to provide crush cans that are progressive, stable,and energy efficient in both high and low speed frontal impact events.

SUMMARY

In accordance with certain embodiments, the present teachings provide amethod for optimizing a twelve-cornered strengthening member comprising:modeling a vehicle assembly including a strengthening member having atwelve-cornered cross section; parameterizing a geometry of thestrengthening member with a plurality of control parameters; defining adesign of experiment using the plurality of control parameters; modelinga vehicle using the vehicle assembly; simulating a frontal impact eventwith the vehicle; generating a response surface based on the frontalimpact event; and determining a set of optimized control parameters forthe strengthening member based on the response surface.

The present teachings additionally or alternatively provide a crush canfor an automotive vehicle, the crush can having a twelve-cornered crosssection comprising sides and corners creating internal angles andexternal angles, wherein a geometry of the cross section varies betweena front section and a rear section of the crush can and is optimizedusing a plurality of control parameters including a lateral width, avertical width, a taper ratio, a front scaling factor, and a rearscaling factor.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not restrictive of the present teachings, as claimed.

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate exemplary embodiments of thepresent teachings and together with the description, serve to explaincertain principles of the teachings.

BRIEF DESCRIPTION OF THE DRAWINGS

At least some features and advantages of the present teachings will beapparent from the following detailed description of exemplaryembodiments consistent therewith, which description should be consideredwith reference to the accompanying drawings, wherein:

FIG. 1 is a cross sectional view of an exemplary embodiment of atwelve-cornered cross section for a strengthening member in accordancewith the present teachings;

FIG. 2 illustrates perspective sectional views of strengthening membersof varying cross sections having a substantially constant thickness andperimeter;

FIG. 3 illustrates perspective sectional views of the exemplary axialcollapse of the strengthening members shown in FIG. 2;

FIG. 4 is a graph of the mean crush force and associated axial crushdistance for exemplary strengthening members having cross sections shownin FIG. 2;

FIGS. 5A-5D illustrate perspective views of vehicle front rails withoutconvolutions, having varying cross sections including twelve-corneredcross sections in accordance with the present teachings;

FIGS. 6A-6D illustrate perspective views of vehicle front rails withconvolutions, having varying cross sections including twelve-corneredcross sections in accordance with the present teachings;

FIG. 7 illustrates comparative cross sectional geometries oftwelve-cornered strengthening members having varying shapes and afour-cornered strengthening member having the same thickness andperimeter;

FIG. 8 is a graph showing the comparison of the crash energy absorbed(for a given force) by strengthening members having the exemplary crosssections illustrated in FIG. 7;

FIG. 9 is a perspective view of a vehicle assembly illustrating astrengthening member in accordance with the present teachings used as acrush can;

FIG. 10 is a perspective view of the crush can of FIG. 9;

FIGS. 11A-11C illustrate a parametric modeling process in accordancewith the present teachings for the crush can of FIG. 10;

FIGS. 12A-12F illustrate how scaling factors in accordance with thepresent teachings can be utilized to change the shape of both a frontand rear section of the crush can of FIG. 10;

FIG. 13 is a logic flow diagram illustrating an exemplary method foroptimizing a crush can in accordance with the present teachings;

FIG. 14 shows results obtained from crash simulations of energy as afunction of average crush force in a displacement domain for variouscrush can designs;

FIGS. 15A-150 illustrate an optimized crush can design; and

FIG. 16 shows results obtained from a crash simulation of force as afunction of displacement for the optimized crush can design of FIGS.15A-150.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Reference will now be made in detail to various embodiments, examples ofwhich are illustrated in the accompanying drawings. The variousexemplary embodiments are not intended to limit the disclosure. To thecontrary, the disclosure is intended to cover alternatives,modifications, and equivalents.

The present teachings contemplate providing a strengthening member witha twelve-cornered cross section having a substantially increasedstiffness throughout the sides and corners without increasing thicknesswithin the corners. The strengthening member can achieve increasedenergy absorption and a more stable axial collapse when forces such asfront and side impact forces are exerted on the strengthening member.The strengthening member can also possess improved durability andnoise-vibration-harshness (NVH) performance due to work hardening on thetwelve corners. The degrees of the internal and external angles of thepresent teachings can achieve the same strength increase as thickenedcorners, while minimizing mass per unit length of the member andmaintaining a high manufacturing feasibility because the member can beformed by bending, rolling, stamping, pressing, hydro-forming, molding,extrusion, cutting, and forging.

An exemplary embodiment of a twelve-cornered cross section for astrengthening member in accordance with the present teachings isillustrated in FIG. 1. As illustrated, the cross section comprisestwelve sides having lengths S₁-S₁₂ and thicknesses T₁-T₁₂, eightinternal corners with angles ν_(i1)-ν_(i8) and four external cornerswith angles ν_(e1)-ν_(e4). The internal and external angular degrees canbe varied to achieve improved strength and other performance features(e.g., stability of folding pattern) compared to existing 90°-angledcross sections. This improved strength can obviate the need forincreased corner thickness, which is an unexpected and unpredictablebenefit of fine-tuning the internal and external angular degrees of astrengthening member having a twelve-cornered cross section. Inaccordance with various embodiments of the present teachings, eachinternal angle can range from about 100° to about 110°, and eachexternal angle can range from about 105° to about 130°. The lengthsS₁-S₁₂ and thicknesses T₁-T₁₂ of the sides can be varied to a certaindegree, as would be understood by one skilled in the art, for example inaccordance with available packaging space within a vehicle.

In certain embodiments of the present teachings, a thickness of thesides and corners can range from about 0.7 mm to about 6.0 mm. Incertain embodiments, the thickness of the sides is substantially thesame as the thickness of the corners.

Conventional strengthening members having square or rectangular crosssections are widely used due to their high manufacturing feasibility.Because a strengthening member with a twelve-cornered cross section inaccordance with the present teachings has substantially increasedstrength and stiffness without requiring thicker corner portions, it hasa higher manufacturing feasibility than previously-contemplatedtwelve-cornered members that have thickened 90° corners. While stillproviding a desired strength, a strengthening member in accordance withthe present teachings can be formed in one or multiple sections by, forexample, bending, rolling, stamping, pressing, drawing, hydro-forming,molding, extrusion, cutting, and/or forging. Thus-formed sections can bejoined via welding, adhesive, fastening, or other known joiningtechnologies.

In accordance with certain exemplary embodiments of the presentteachings, the thickness of the strengthening member may vary, forexample, within one side or from side to side to optimize the overallaxial crush and bending performance. Examples of such varied thicknessembodiments are illustrated in FIGS. 5D and 6D, which are described indetail below.

In comparing crash energy absorption of strengthening members of varyingshapes having the same thickness and perimeter, as illustrated in FIG.2, for example for an impact with a rigid wall at 35 mph, atwelve-cornered cross section in accordance with the present teachingsdemonstrated the shortest crush distance and smallest folding length. Atwelve-cornered cross section in accordance with the present teachingsalso demonstrated the most stable axial collapse and the highest crashenergy absorption. In fact, a twelve-cornered cross section inaccordance with the present teachings can achieve about a 100% increasein crash energy absorption over a square cross section and a 20-30%increase in crash energy absorption over hexagonal and octagonal crosssections. FIG. 3 illustrates an exemplary axial collapse of thestrengthening members shown in FIG. 2. As can be seen, the strengtheningmember having a twelve-cornered cross section in accordance with thepresent teachings exhibits the shortest crush distance and most stablefolding pattern.

FIG. 4 illustrates a graph of mean crush force for an impact with arigid wall at 35 mph, in kN, exerted axially on exemplary strengtheningmembers having the cross sections shown in FIG. 2. As can be seen, astrengthening member having a twelve-cornered cross section inaccordance with the present teachings can sustain a much higher crushingforce for a given resulting crushing distance. This allows improvedimpact energy management while minimizing mass per unit length.

A twelve-cornered cross section in accordance with the present teachingsis contemplated for use with a number of structural members such as afront rail, a side rail, a cross member, roof structures, and othercomponents that can benefit from increased crash energy absorption. Inaddition, the present teachings can be applied to both body-on-frame andunitized vehicles, or other types of structures.

FIGS. 5A-5D illustrate exemplary embodiments of a vehicle front railhaving a cross section in accordance with the present teachings. Thefront rail is of a type without convolutions. FIG. 5A illustrates afront rail having a known, substantially rectangular cross section withfour corners 510, 512, 514, 516 of about ninety degrees, and four sides520, 522, 524, 526. FIGS. 5B through 5D illustrate front rails havingtwelve-cornered cross sections in accordance with the present teachings,the corner indentations I2 in FIG. 5C being greater than theindentations I1 in FIG. 5B. In these illustrated exemplary embodiments,the rails have a two-part construction comprising pieces A and B. Thepresent teachings contemplate rails of other construction such asone-piece or even 3-or-more piece construction, the number of pieces inFIGS. 5A through 5D being exemplary only.

The embodiments of FIGS. 5B and 5C include top and bottom sides. S_(T)and S_(B) respectively, having substantially the same length as eachother, and left and right sides, S_(L) and S_(R) respectively, alsohaving substantially the same length as each other. Piece A includesright side S_(R), part of bottom side S_(B), and part of top side S_(T).Piece B includes left side S_(L), part of bottom side S_(B), and part oftop side S_(T). To simplify FIGS. 5B-5D, all of the sides S₁ through S₁₀illustrated in FIG. 1 are not labeled but are of course present.Similarly, the eight internal corners (angles: ν_(i1)-ν_(i8)) and fourexternal corners (angles: ν_(e1)-ν_(e4)) illustrated in FIG. 1 are notlabeled but are present.

FIG. 5D illustrates a front rail having a twelve-cornered cross section,the rail being formed with different depths of indentations, for exampleto accommodate packaging constraints of a vehicle's engine compartment.In accordance with such an embodiment needing to have a varied shape toaccommodate engine compartment constraints, to achieve optimized axialcrush performance, the thicknesses of the sides, angles of the corners,and indentation depths can all be adjusted to provide optimal strength,size and shape. In the example of FIG. 5D, corner indentations I3 and I4have different depths, corner indentation I4 being shallower than cornerindentation I3. Corner indentations I5 and I6 have substantially thesame depth as each other, that depth differing from the depths of cornerindentations I3 and I4. The top and bottom sides, S_(T) and S_(B)respectively, have different lengths, with top side S_(T) being longerthan bottom side S_(B), and the left and right sides. S_(L) and S_(R)respectively, have differing lengths, with right side S_(R) being longerthan left side S_(L). The present teachings also contemplate atwelve-cornered cross section where each of the corner indentations hasa different depth and a different angle, and each of the sides has adifferent length, or where some of the sides have the same length andsome of the corner indentations have the same depth and perhaps the sameinternal and external angles.

For a front rail comprising SAE1010 material, a front rail asillustrated in FIG. 5B (with shallower indentations) can save, forexample, about 17% weight compared to a square or rectangular crosssection, and a front rail as illustrated in FIG. 5C (with deeperindentations) can save, for example, about 35% weight. For a front railcomprising DP600 material, a front rail as illustrated in FIG. 5B (withshallower indentations) can save, for example, about 23% weight and afront rail as illustrated in FIG. 5C (with deeper indentations) cansave, for example, about 47% weight. Such weight savings are realizedbecause the increased strength of the twelve-cornered cross sectionallows the use of a thinner gauge material to provide the same strength.

FIGS. 6A-6D illustrate exemplary embodiments of a vehicle front railhaving a cross section in accordance with the present teachings. Thefront rail is of a type with convolutions. FIG. 6A illustrates aconvoluted front rail having a known, substantially rectangular crosssection with four corners 610, 612, 614, 616 of about ninety degrees,and four sides 620, 622, 624, and 626. FIGS. 6B through 6D illustrateconvoluted front rails having twelve-cornered cross sections inaccordance with the present teachings, the corner indentations I8 inFIG. 6C being greater than the indentations I7 in FIG. 6B. In theseillustrated exemplary embodiments, the rails have a two-partconstruction with pieces C and D. As stated above, the two-piececonstructions shown in FIGS. 6B through 6D are exemplary only and thepresent teachings contemplate rails of other construction such asone-piece or even 3-or-more piece construction.

The embodiments of FIGS. 6B and 6C include top and bottom sides. S_(T)and S_(B) respectively, having substantially the same length as eachother, and left and right sides, S_(L) and S_(R) respectively, alsohaving substantially the same length as each other. Piece C includesright side S_(R), part of bottom side S_(B), and part of top side S_(T).Piece D includes left side S_(L), part of bottom side S_(B), and part oftop side S_(T). To simplify FIGS. 6B-6D, all of the sides S₁ throughS₁₀, as illustrated in FIG. 1, are not labeled but are present.Similarly, the eight internal corners (angles: ν_(i1)-ν_(i8)) and fourexternal corners (angles: ν_(e1)-ν_(e4)) as illustrated in FIG. 1, arenot labeled but are present.

FIG. 6D illustrates a convoluted front rail having a twelve-corneredcross section, the rail being formed with different depths ofindentations, for example to accommodate packaging constraints of avehicle's engine compartment. In accordance with such an embodimentneeding to have a varied shape to accommodate engine compartmentconstraints, to achieve optimized axial crush performance, thethicknesses of the sides, angles of the corners, and indentation depthscan all be adjusted to provide optimal strength, size and shape. In theexample of FIG. 60, corner indentations I9 and T10 have differentdepths, with corner indentation I10 being shallower than cornerindentation I9. Corner indentations I11 and I12 have substantially thesame depth as each other, that depth differing from the depths of cornerindentations I9 and I10. The top and bottom sides, S_(T) and S_(B)respectively, have different lengths, with top side Si being longer thanbottom side S_(B), and the left and right sides, S_(L) and S_(R)respectively, have differing lengths, with right side S_(R) being longerthan left side S_(L). The present teachings also contemplate atwelve-cornered cross section where each of the corner indentations hasa different depth and a different angle, and each of the sides has adifferent length, or where some of the sides have the same length andsome of the corner indentations have the same depth and perhaps the sameinternal and external angles.

For a convoluted front rail comprising SAE1010 material, a front rail asillustrated in FIG. 6B (with shallower indentations) can save, forexample, about 20% weight compared to a square or rectangular crosssection, and a front rail as illustrated in FIG. 6C (with deeperindentations) can save, for example, about 32% weight. For a convolutedfront rail comprising DP600 material, a front rail as illustrated inFIG. 6B (with shallower indentations) can save, for example, about 30%weight and a front rail as illustrated in FIG. 6C (with deeperindentations) can save, for example, about 41% weight.

Strengthening members having a variety of cross sections are illustratedin FIG. 7. As can be seen, CAE006 has a twelve-cornered cross sectionwith external angles of 90°. CAE007 has a twelve-cornered cross sectionwith external angles of 108°in accordance with the present teachings.CAE008 has a twelve-cornered cross section with external angles of 124°in accordance with the present teachings. CAE009 has a twelve-corneredcross section with external angles of 140°. CAE010 has a twelve-corneredcross section with external angles of 154°. Finally, CAE011 has a squarecross section. A comparison of the axial crush strength of theillustrated square and twelve-cornered cross sections having differingexternal angles is illustrated in FIG. 8. As can be seen, the overallaxial crush strength of the strengthening member having atwelve-cornered cross section is far greater than that of thestrengthening member having a square cross section.

As can further be seen, the exemplary strengthening members withtwelve-cornered cross sections having external angles of 108° and 124°show an overall increase in axial crush strength over twelve-corneredcross sections having external angles of 90°. In fact, deviation of theangles from 90° such that each internal angle is about the same as otherinternal angles and ranges from about 100° to about 110°, and eachexternal angle is about the same as other external angles and rangesfrom about 105° to about 130°, increases strength without negativelyaffecting the stability of a crush mode of the strengthening member.Such an increase in strength obviates the need for reinforcing (e.g.,thickening) the concave portions at the four corners of thestrengthening member, decreasing weight and cost and increasingmanufacturing feasibility.

Strengthening members in accordance with the present teachings cancomprise, for example, steel, aluminum, magnesium, fiberglass, nylon,plastic, a composite, or any other suitable materials. Exemplaryimplementations of the strengthening member can comprise, for example, ahigh strength steel such as, for example, DP590, DP590R, or HSLA350.These three steels have similar yield strengths, but DP590 and DP590Rhave a higher tensile strength than HSLA350. DP590R has aferrite-bainite microstructure and a slightly higher yield-to-tensilestrength ratio than DP590.

In various applications, strengthening members, as detailed above, canbe used as crush cans to manage impact energy and intrusion during afrontal collision. FIG. 9, for example, is a perspective view of avehicle assembly 100 including a bumper 101 and crush cans 102. Crushcans 102 can be attached directly to a bumper beam 103 aligned with avehicle's front rails (not shown). As shown in FIG. 10, the crush can102 can have a twelve-cornered cross-section comprising sides 104 andcorners 105 creating internal angles ν_(ij) and external angles ν_(ej).As illustrated in FIG. 1, for example, the cross section may comprisetwelve sides having lengths S₁-S₁₂ and thicknesses T₁-T₁₂, eightinternal corners with angles ν_(i1)-ν_(i8) and four external cornerswith angles ν_(e1)-ν_(e4). Those of ordinary skill in the art wouldunderstand that the embodiments illustrated in FIGS. 9 and 10 areexemplary only, and that a crush can in accordance with the presentteachings may have various geometries (i.e., cross-sections) and canhave various locations and/or configurations within a vehicle bumperassembly.

In accordance with certain embodiments of the present teachings, whenusing a twelve-cornered strengthening member as a crush can, the designof the crush can may be optimized to provide a desired crush result(i.e., with respect to energy absorption and crush distance) for bothhigh and low speed frontal impact events.

As used herein, the term high speed frontal impact event refers to acrash wherein the front end of a vehicle impacts an object at a highspeed, such as, for example, a crash wherein the front end of a vehicleimpacts an object while the vehicle is going at least 30 mph. As thoseof ordinary skill in the art would understand, such events may besimulated, for example, by various high speed frontal crash modes tests)designed to meet occupant injury metrics. Such modes, may include, forexample, a 35 mph, 100% overlap, frontal rigid barrier mode (i.e.,running a vehicle into a solid barrier at 35 mph); a 40 mph, 40% offset,deformable barrier mode (i.e., running a vehicle into a deformablebarrier at 40 mph with a 40% offset so that only 40% of the front end ofthe vehicle impacts the barrier); and a 25-30 mph, 30° angular, rigidbarrier mode (i.e., running a vehicle into a solid barrier at 25-30 mphand a 30° angle).

As used herein, the term low speed frontal impact event refers to acrash wherein the front end of a vehicle impacts an object at a lowspeed, such as, for example, a crash wherein the front end of a vehicleimpacts an object while the vehicle is going 10 mph or less. As those ofordinary skill in the art would understand, such events may besimulated, for example, by various low speed frontal crash modes (i.e.,tests) designed with objectives of minimizing the repair costs of avehicle. Such modes may include, for example, a 15 kph (9.32 mph), 40%offset, 10° angular, rigid barrier mode (i.e., running a vehicle into asolid barrier at 15 kph and a 10° angle, with a 40% offset so that only40% of the front end of the vehicle impacts the barrier).

In certain exemplary embodiments of the present teachings, the geometryof a cross section of a crush can be optimized using a plurality ofcontrol parameters. The control parameters may be generated, forexample, using a parametric model of the crush can. As would beunderstood by those of ordinary skill in the art, any type of3-dimensional structural modeling software and/or tools may be used tocreate the parametric model.

As shown below in Table 1 and illustrated in FIGS. 11A-11C, in certainembodiments, the geometry of the crush can may be parameterized withfive control parameters, such as, for example, a lateral width(Width_y), a vertical width (Width_z), a taper ratio, a front scalingfactor, and a rear scaling factor.

TABLE 1 Summary of Control Parameters Parameter Baseline Lower BoundUpper Bound Width_y 0 −5 mm 15 mm Width_z 0 −5 mm 15 mm Taper Ratio 1.00.7 1.2 Front Scaling 1.0 0.5 2.0 Factor Rear Scaling 1.0 0.5 2.0 Factor

As illustrated in FIG. 11A, starting from a baseline twelve-corneredgeometry (shown by the solid line), a front section 106 of the crush can102 may be parameterized in both a lateral (Y) direction and a vertical(Z) direction by adjusting a lateral width (Width-y) and a verticalwidth (Width-z). Adjusting such parameters provides a dimensional changefor the front section 106 of the crush can 102 as illustrated by thedotted line in FIG. 11A. In other words, the lateral and vertical widthsmay comprise new dimensions for the front section 106 of the crush can102. As shown in Table 1, based on a defined design of experiment (DOE)for a particular design application, the dimensions of the front section106 of the crush can 102 may be changed by varying the lateral andvertical widths (Width_y and Width_z, respectively) between an upper andlower bound. In certain embodiments, for example, the lateral width ofthe front section 106 may be varied in a range of about −5 mm from abaseline lateral width to about 15 mm from the baseline lateral width;and the vertical width of the front section 106 may be varied in a rangeof about −5 mm from a baseline vertical width to about 15 mm from thebaseline vertical width.

As illustrated in FIG. 11B, a taper ratio may then be used to raise orlower the height ratio between the front section 106 and a rear section107 of the crush can 102. In this parameterization process, coordinatesy₀ and z₀ of the rear section 107 of the crush can 102 are multiplied bya given taper ratio to form new coordinates y* and z*. As shown in Table1, based on the defined DOE, the coordinates y₀ and z₀ may be multipliedby a taper ratio between an upper and lower bound. In certainembodiments, for example, the coordinates y₀ and z₀ may be multiplied bya taper ratio in a range of about 0.74 (i.e., to raise the height ratiobetween the front and rear sections) to about 1.2 (i.e., to lower theheight ratio between the front and rear sections). As would beunderstood by those of ordinary skill in the art, corner points betweenthe front section 106 and the rear section 107 of the crush can 102 maythen be connected to create an intermediate profile along a longitudinalaxis of the crush can 102.

As illustrated in FIG. 110, a scaling factor may then be applied to boththe front section 106 and the rear section 107 of the crush can 102. Inother words, to adjust the shape of the front section 106, a frontscaling factor may be applied to coordinates of the front cross section106; and to adjust the shape of the rear cross section 107, a rearscaling factor may be applied to coordinates of the rear section 107.For explanation purposes, FIG. 11C generically represents both the frontsection 106 and the rear section 107 of the crush can 102. In thisparameterization process, as shown in FIG. 11C, radial directions R maybe defined between a center point C of each section (front and rear) andinner corner points I₀ of each section. Coordinates y₀ and z₀ of theinner corner points I₀ may then be multiplied by a given scaling factorto form new coordinates y* and z* for new inner corner points I*. Asshown in Table 1, based on the defined DOE, the coordinates y₀ and z₀for each section (front and rear) may be multiplied by a scaling factorbetween an upper and lower bound. In certain embodiments, for example,the coordinates y₀ and z₀ of the front section 106 may be multiplied bya front scaling factor in a range of about 0.5 to about 2.0; andcoordinates y₀ and z₀ of the rear section 107 may be multiplied by arear scaling factor in a range of about 0.5 to about 2.0. As illustratedby the dotted line in FIG. 11C, the shape of each section (front andrear) may then be adjusted by connecting the new inner corner points I*for each section to adjacent outer corner points O for each section.

FIGS. 12A-12F illustrate, for example, how scaling factors in accordancewith the present teachings can be utilized to change the shape of afront section 106 and rear section 107 of a crush can 102A-F. FIG. 12Ashows a baseline shape, as illustrated in FIG. 10, wherein the frontscaling factor is 1 and the rear scaling factor is 1. FIGS. 12B-12F showmorphed shapes, wherein the front and rear scaling factors are varied ina range of about 0.5 to about 2.0 (i.e., between the upper and lowerbound as shown in Table 1). FIG. 12B, for example, shows a morphedshape, wherein the front scaling factor is 0.751 and the rear scalingfactor is 1.392. Those of ordinary skill in the art would understand,that the embodiments of FIGS. 12A-12F are exemplary only, and thatscaling factors are variable and dependent upon a particular DOE.Accordingly, those of ordinary skill in the art would understand thatthe geometry of a crush can may take on various shapes, dimensions,and/or configurations throughout the parameterization process withoutdeparting from the scope of the present teachings and claims.Furthermore, as illustrated in FIGS. 12B-12F, in certain embodiments,the geometry of the cross section may vary between a front section and arear section of the crush can.

FIG. 13 is a logic flow diagram depicting an exemplary method foroptimizing a strengthening member, such as, for example, atwelve-cornered crush can 102, in accordance with the parametricmodeling process described above. As shown at step 200 in FIG. 13, avehicle assembly including a twelve-cornered strengthening member (e.g.,a vehicle assembly 100 as depicted in FIG. 9, including a bumper 103 anda crush can 102) is modeled, for example using a finite element model.The present teachings contemplate using any known methods and/ortechniques as would be understood by those of ordinary skill in the artto build a finite element model of the vehicle assembly 100. Certainexemplary embodiments of the present teachings consider, for example,building the finite-element model using AutoCAD® developed by Autodesk®or other computer-aided design (CAD) based software applications.

At step 201, the crush can 102 is parameterized using a parametricmodeling tool. The present teachings contemplate using any known methodsand/or techniques as would be understood by those of ordinary skill inthe art to build a parametric model of the crush can 102. Certainexemplary embodiments of the present teachings consider, for example,building the parametric model using MeshWorks developed by DetroitEngineered Products Inc. (DEP) or Pro/ENGINEER developed by FTC®.

As explained in detail above, the geometry of the crush can 102 can beparameterized with a plurality of control parameters. In certainembodiments, for example, the geometry of the crush can 102 may beparameterized by generating a lateral width (Width_y), a vertical width(Width_z), a taper ratio, a front scaling factor, and a rear scalingfactor. As above, the lateral width and the vertical width may generatedimensions for a front section 106 of the crush can 102 (see FIG. 11A),the taper ratio may generate a height ratio between the front section106 and a rear section 107 of the crush can 102 (see FIG. 11B), thefront scaling factor may scale coordinates y₀ and z₀ of inner cornerpoints I₀ of the front section 106 of the crush can 102 (see FIG. 11C),and the rear scaling factor may scale coordinates y₀ and z₀ of innercorner points I₀ of the rear section 107 of the crush can 102 (see FIG.11C).

As shown at step 202 of FIG. 13, a design of experiment (DOE) is definedusing the plurality of control parameters. As those of ordinary skill inthe art would understand, DOE is a systematic approach to theinvestigation of a system or process. The DOE may, for example, utilizea series of structured tests to make planned changes to input variablesto the system or process, while assessing the effects of the changes ona pre-defined output. In other words, DOE is a methodology thatmaximizes the knowledge gained from experimental data, allowing a userto extract a large amount of information from a limited number of testruns. To optimize a design, for example, the DOE may provide anoptimization algorithm with an initial population of designs from whichthe algorithm can “learn” (i.e., the DOE may provide the initial datapoints). Accordingly, as those of ordinary skill in the art wouldunderstand, defining a DOE may comprise generating structured datatables (i.e., tables that contain an amount of structured variation) tobe used as a basis for multivariate modeling. As illustrated in Table 1,for example, in certain embodiments, the DOE may define an upper boundvalue and a lower bound value for each of the control parameters. Inother words, the DOE defines various designs, each design comprising acombination of the five control parameters (i.e., lateral width(Width_y), vertical width (Width_z), taper ratio, front scaling factor,and rear scaling factor), wherein each of the five control parameters isbounded by the defined upper and lower bound. Accordingly, as shown atstep 203, the DOE outputs various combinations of the five controlparameters to the model of the bumper/crush can assembly 100 (i.e., thebumper/crush can assembly 100 may be updated with various combinationsof control parameters). The present teachings contemplate using anyknown methods and/or techniques as would be understood by those ofordinary skill in the art to define the DOE. Certain exemplaryembodiments of the present teachings consider, for example, usingModeFRONTIER™ developed by ESTECO, Isight developed by SIMULIA, orvarious other multi-objective optimization and design applicationswritten to couple CAD tools, finite element structural analysis, and/orcomputational fluid dynamics.

At step 204, a vehicle is modeled, for example, using a finite elementmodel based on the DOE (e.g., a vehicle subsystem or a full vehicle ismodeled using a bumper/crush can assembly). As above, the presentteachings contemplate using any known methods and/or techniques as wouldbe understood by those of ordinary skill in the art to build a finiteelement model of the vehicle.

As shown at step 205 of FIG. 13, a frontal impact event is simulatedwith the vehicle model. The present teachings contemplate using anyknown methods and/or techniques as would be understood by those ofordinary skill in the art to simulate the frontal impact event. Certainexemplary embodiments of the present teachings consider, for example,simulating a crash using LS-DYNA® simulation software developed byLivermore Software Corp, RADIOSS™ offered by Altair Engineering Inc.PAM-CRASH developed by ESI Group, or Abaqus/Explicit developed bySIMULIA. During each simulation, a performance output is measured forthe crush can 102, subject to the frontal impact event, as indicated atstep 206. As those of ordinary skill in the art would understand, asused herein the term “performance output” refers to outputs of interest(i.e., from the simulation), which are used to measure or quantify theperformance or functionality of the part being optimized (e.g., thecrush can 102). In certain embodiments, for example, the outputs ofinterest include a mass of the can 102 (i.e. a mass increase or decreasefrom baseline) that is measured with relation to energy absorption(i.e., an amount of internal energy absorbed by the crush can 102 duringthe course of its deformation) and an average crush force of the crushcan 102 (i.e., the average force needed to crush the crush can 102). Incertain additional embodiments, the outputs of interest include a lengthof the crush can 102 that has been crushed. Furthermore, the performanceoutput may be measured during both high and low speed frontal impactevents.

At step 207, a response surface is generated based on the performanceoutput from the simulation. As those of ordinary skill in the art wouldunderstand, response surface methods (RSMs) are generally used toexamine the “surface” or the relationship between a simulated responseand the factors affecting the response. Regression models are used, forexample, to analyze the response, focusing on the nature of therelationship between the response and the input factors rather thanidentification of important input factors. Accordingly, an RSM tries tointerpolate available test data in order to locally or globally predictthe correlation between the control parameters and the optimizationobjectives (i.e., the optimization problem). The present teachingscontemplate using any known methods and/or techniques as would beunderstood by those of ordinary skill in the art to generate theresponse surface. Certain exemplary embodiments of the present teachingsconsider, for example, generating the response surface using amulti-objective optimization application, such as ModeFRONTIER™.

As would be understood by those of ordinary skill in the art, a set ofoptimized control parameters (i.e., for the crush can 102) may bedetermined based on the response surface. As indicated at step 208 ofFIG. 13, for example, based on a particular application, an optimizationproblem is defined for the crush can 102. In certain exemplaryembodiments, based on vehicle type and/or application, designobjectives, design constraints, and design variables for the crush can102 may be defined within the optimization application. As shown at step209, a set of optimized control parameters is determined by searchingfor a solution to the optimization problem based on the responsesurface. In other words, the optimization application may performvarious virtual runs searching for a solution to the optimizationproblem. As would be understood by those of ordinary skill in the art,as used herein the term “virtual runs” refers to the process ofpredicting performance outputs for a design (i.e., a set of optimizedcontrol parameters) using the response surface (i.e., based on theoutputs extracted from actual simulations).

In accordance with certain exemplary embodiments of the presentteachings, as shown at step 210, the determined set of optimized controlparameters may be validated, for example, by performing a confirmationrun. As above, a crush can 102 may be modeled using the optimizedcontrol parameters, a frontal impact event may be simulated with avehicle model including the crush can 102, and a performance output maybe measured for the crush can 102. If the crush can's performance isacceptable, the optimization application may generate an optimum designfor the crush can 102, as indicated by the last step 211, shown in theflow diagram of FIG. 13.

As those of ordinary skill in the art would understand, the above methodis exemplary only and not intended to be construed as requiring that itssteps be performed in a specific order. Accordingly, where a methodclaim does not actually recite an order to be followed by its steps, orit is not otherwise specifically stated in the claims or descriptionsthat the steps are to be limited to a specific order, it is no wayintended that any particular order be inferred. Furthermore, the presentteachings and claims are not intended to be limited to the above recitedsteps, and may include various additional steps and/or combinations ofsteps as would be understood by those of ordinary skill in the art.

Example

To further demonstrate the above optimization method, an exemplary crushcan was modeled and experimental test runs were conducted, as shown anddescribed below with reference to Table 2 and FIGS. 14-16.

TABLE 2 Summary of Optimization Parameter/Performance Baseline OptimalWidth_y 0 10.88 Width_x 0 5.65 Taper Ratio 1.0 1.11 Front Scaling Factor1.0 1.46 Rear Scaling Factor 1.0 0.95 Mass (Kg) 1.32 1.34 Average CrushForce (KN) 86.3 109.2 Energy Absorption (J) 15381 19230

As illustrated in Table 2, to optimize a twelve-cornered crush can, abumper/crush can assembly was modeled and the geometry of the crush canwas parameterized, establishing a set of baseline control parameters(Width_y=0, Width_z=0, taper ratio=1, front scaling factor=1.0, and rearscaling factor=1.0). To create a complete crush model, a vehiclesubsystem, including the bumper/crush can assembly, was modeled as arigid body (i.e., a body having nothing to deform behind it) with alumped mass of 401 Kg at the vehicle's center of gravity. To establish aset of baseline performance outputs (a 1.32 Kg crush can with an 86.3 KNaverage crush force and 15381 J of energy absorption), a frontal impactevent was simulated using a 35 mph, 100% overlap, frontal rigid barriermode (i.e., the vehicle was run into a wall at an initial velocity(I.V.) of about 35 mph) to completely crush the crush cans.

Based on the defined DOE (see Table 1), the frontal impact event wasthen simulated using various combinations of the five control parameters(i.e., the bumper/crush can assembly was updated with variouscombinations of control parameters) to generate a response surface. Tooptimize the crush can dimensions, an optimization problem was definedto minimize the mass of the crush can, while providing energy absorptionof greater than about 15 KJ for each can, and an average crush force ofgreater than about 100 KN and less than about 110 KN per can.

As illustrated in FIG. 14, both “real” and “virtual” simulations wererun, wherein real simulation results were obtained from actualsimulation results (i.e., run using the DOE) and virtual simulationresults were obtained from the optimizer returning solutions based onthe response surface (i.e., fitted using actual simulation results). Asshown, feasible solutions were identified based on the optimizationproblem (i.e., solutions which satisfied the energy and forceconstraints). FIG. 14 illustrates how energy absorption varied withaverage crush force, which was measured, for example, based on thedisplacement domain (avgf_disp). As shown, energy absorption increasedwith an increase in the average crush force.

There was, however, an imposed force constraint of 110 KN (e.g., toprevent deformation of rails behind the crush cans). Accordingly, asshown in FIG. 14, solutions which maximized energy absorption within theforce constraint were identified as feasible solutions. In other words,as would be understood by those of ordinary skill in the art, a paretoplot, as defined, for example, in the optimization software, was used tosee how the design solutions would fall by simultaneously plotting twoobjective functions. The numbers 11 and 13, for example, were the designsolutions which satisfied the optimization problem. To determine a setof corresponding control parameters (i.e., a set of optimized controlparameters) for design numbers 11 and 13, a design variables table canthen be consulted as would be understood by those of ordinary skill inthe art.

As shown in FIGS. 15A-15C, a crush can 202 was then modeled (i.e.,having a front section 206 and a rear section 207) using the optimizedcontrol parameters, and a frontal impact event was simulated with thevehicle subsystem model including the crush can 202. The results of thefrontal impact event are shown in FIG. 16. As illustrated in FIG. 16, anacceptable performance output (force (KN) vs. x-displacement (mm)) wasmeasured for the crush can 202 (i.e., the imposed force constraint of110 KN was met between about 100 to about 200 mm of crush).

In accordance with certain embodiments, to reduce complexity and savecomputation time, a sub-system model can be utilized to track crush canperformance in a high speed frontal impact event by imposing derivedconstraints from a low speed frontal impact event (e.g., accounting forthe carry-over strength from a vehicle's side-rails). For example, usingan average side rail strength of about 130 KN, the strength of the crushcan may be set at a lower level (e.g., 110 KN or less) to insure thatthe crush can crushed first (prior to the side rails). Accordingly, thecrush or stroke during a low speed frontal impact event can beinherently minimized by maximizing the crush strength for the crush can(e.g., within the designated constraint). Thus, although both low speedand high speed crashes may be simulated using the above method (e.g.,through simultaneous optimizations), a simple high speed model may trackthe high speed response and optimize the design to maximize energyabsorption through the entire crush distance with a reduced crush canweight. The improved performance of the crush can may then be verifiedby spot checking a low speed event (i.e., since the low speedrequirements were backed into the optimization problem in the form ofconstraints to the force level attained).

Thus, the method illustrated above with regard to Table 2 and FIGS.14-16 demonstrates how to optimize a twelve-cornered strengtheningmember to provide a desired crush result in terms of energy absorptionand crush distance. Accordingly, methods for optimizing atwelve-cornered strengthening member in accordance with the presentteachings can be implemented to provide crush cans that are progressive,stable, and energy efficient in both high and low speed frontal impactevents. Those having ordinary skill in the art would understand theoptimization problem described above and the crash mode used areexemplary only and that other optimization problems and/or crash modesmay be chosen depending on various factors without departing from thepresent teachings.

Although various exemplary embodiments shown and described herein relateto methods for optimizing a twelve-cornered crush can in an automobilebumper assembly, those having ordinary skill in the art would understandthat the methodology described may have a broad range of application tostrengthening members useful in a variety of applications. Ordinarilyskilled artisans would understand, for example, how to modify theexemplary methods described herein to optimize the geometry of astrengthening member used in an application other than a bumperassembly.

Accordingly, while the present teachings have been disclosed in terms ofexemplary embodiments in order to facilitate a better understanding, itshould be appreciated that the present teachings can be embodied invarious ways without departing from the scope thereof. Therefore, thepresent teachings should be understood to include all possibleembodiments which can be embodied without departing from the scope ofthe teachings set out in the appended claims.

For the purposes of this specification and appended claims, unlessotherwise indicated, all numbers expressing quantities, percentages orproportions, and other numerical values used in the specification andclaims, are to be understood as being modified in all instances by theterm “about.” Accordingly, unless indicated to the contrary, thenumerical parameters set forth in the written description and claims areapproximations that may vary depending upon the desired propertiessought to be obtained by the present teachings. At the very least, andnot as an attempt to limit the application of the doctrine ofequivalents to the scope of the claims, each numerical parameter shouldat least be construed in light of the number of reported significantdigits and by applying ordinary rounding techniques.

It is noted that, as used in this specification and the appended claims,the singular forms “a,” “an,” and “the,” include plural referents unlessexpressly and unequivocally limited to one referent. As used herein, theterm “include” and its grammatical variants are intended to benon-limiting, such that recitation of items in a list is not to theexclusion of other like items that can be substituted or added to thelisted items.

It will be apparent to those skilled in the art that variousmodifications and variations can be made to the devices and methods ofthe present disclosure without departing from the scope of itsteachings. Other embodiments of the disclosure will be apparent to thoseskilled in the art from consideration of the specification and practiceof the teachings disclosed herein. It is intended that the specificationand embodiment described herein be considered as exemplary only.

What is claimed is:
 1. A crush can for an automotive vehicle, the crushcan having a twelve-cornered cross section comprising sides and cornerscreating internal angles and external angles, wherein a geometry of thecross section varies between a front section and a rear section of thecrush can and is optimized using a plurality of control parametersincluding a lateral width, a vertical width, a taper ratio, a frontscaling factor, and a rear scaling factor.
 2. The crush can of claim 1,wherein the internal angles of the front section of the crush can arenot the same as the internal angles of the rear section of the crushcan, and the external angles of the front section of the crush can arenot the same as the external angles of the rear section of the crushcan.
 3. The crush can of claim 1, wherein the lateral width of the frontsection of the crush can is not the same as the lateral width of therear section of the crush can and the vertical width of the frontsection of the crush can is not the same as the vertical width of therear section of the crush can.
 4. The crush can of claim 3, wherein thetaper ratio raises or lowers a height ratio between the front sectionand a rear section of the crush can.
 5. The crush can of claim 4,wherein the front scaling factor scales coordinates of inner cornerpoints of the front section of the crush can and the rear scaling factorscales coordinates of inner corner points of the rear section of thecrush can.
 6. The crush can of claim 1, wherein the plurality of controlparameters are generated using a parametric model of the crush can. 7.The crush can of claim 6, wherein the geometry of the cross section isoptimized using an optimization algorithm for an optimal crush canperformance with respect to energy absorption and crush distance forboth high and low speed frontal impact events.
 8. A method foroptimizing a twelve-cornered strengthening member, the methodcomprising: modeling a vehicle assembly including a strengthening memberhaving a twelve-cornered cross section; parameterizing a geometry of thestrengthening member with a plurality of control parameters; defining adesign of experiment using the plurality of control parameters; modelinga vehicle using the vehicle assembly; simulating a frontal impact eventwith the vehicle; generating a response surface based on the frontalimpact event; and determining a set of optimized control parameters forthe strengthening member based on the response surface.
 9. The method ofclaim 8, wherein modeling the vehicle assembly comprises modeling abumper and a crush can having a twelve-cornered cross section.
 10. Themethod of claim 8, wherein parameterizing the geometry with a pluralityof control parameters comprises generating a lateral width, a verticalwidth, a taper ratio, a front scaling factor, and a rear scaling factor.11. The method of claim 10, wherein generating the lateral width and thevertical width comprises generating dimensions for a front section ofthe strengthening member.
 12. The method of claim 11, wherein generatingthe taper ratio comprises generating a height ratio between the frontsection and a rear section of the strengthening member.
 13. The methodof claim 12, wherein generating the front scaling factor comprisesgenerating a factor which scales coordinates of inner corner points ofthe front section of the strengthening member and generating the rearscaling factor comprises generating a factor which scales coordinates ofinner corner points of the rear section of the strengthening member. 14.The method of claim 8, wherein defining a design of experiment comprisesdefining an upper bound value and a lower bound value for each of theplurality of control parameters.
 15. The method of claim 8, whereinmodeling a vehicle using the vehicle assembly comprises modeling avehicle subsystem or a full vehicle based on the design of experiment.16. The method of claim 8, wherein simulating a frontal impact eventwith the vehicle comprises measuring a performance output of thestrengthening member during a high speed frontal impact event and/or alow speed frontal impact event.
 17. The method of claim 16, whereinmeasuring a performance output of the strengthening member comprisesmeasuring energy absorption, an average crush force, and a mass of thestrengthening member.
 18. The method of claim 17, wherein determiningthe set of optimized control parameters comprises defining anoptimization problem including design objectives, design constraints,and design variables for the strengthening member.
 19. The method ofclaim 18, wherein determining the set of optimized control parameterscomprises searching for a solution to the optimization problem based onthe response surface.
 20. The method of claim 8, further comprisingvalidating the set of optimized control parameters by simulating afrontal impact event with the set of optimized control parameters.